Afunction f is given by the formula f(x)=a⋅ekx for constants a and k. we also know that f(4)=12 and f(7)=5. find numerical values for the constants a and k.

The given function is

And it is given that

On using this information, we will get

And the other point is

Using this point, we will get

Dividing both equations, we will get

Taking ln to both sides

Performing back substitution ,

(a) the volume of the cone is 20/3 in3

hence, option a is correct.